Edelweiss Applied Science and Technology 
ISSN: 2576-8484 
Vol. 8, No. 5, 922-939 
2024 
Publisher: Learning Gate 
DOI: 10.55214/25768484.v8i5.1794 
© 2024 by the author; licensee Learning Gate 

© 2024 by the author; licensee Learning Gate 
* Correspondence:  wiwin62@gmail.com 

 
 
 
 
 

Prediction of queue length due to lane closure with shockwave analysis on 
Jagorawi toll road (Case study: Km 19+600) 

 
Endang Widjajanti 
Master of Civil Engineering Study Program, National Institute of Science and Technology, Indonesia; wiwin62@gmail.com () 

 

 

Abstract: This study discusses the prediction of queue length with shockwave analysis through traffic 
flow characteristics on the Jagorawi toll road KM 19+600. The purpose of this study is to analyze the 
relationship between traffic characteristics (current, density and speed) on the Jagorawi KM19+600 toll 
road and evaluate the value of shock waves due to the narrowing of the road on the Jagorawi KM 
19+600 toll road when the lane is closed. The method used to achieve the purpose of this study is to use 
the linear regression method to determine the relationship between traffic variables through the 
Greenshield model. The data obtained was obtained from CCTV data recording at KM 19 + 600. The 
results of the current-velocity-density relationship analysis show that the selected model for the 
relationship is the Greenshield model with a maximum current of 9574 pcu/hour. From the results of 
the shock wave simulation for the closure of 1 lane, 2 lanes and 3 lanes with the same flow, namely 7200 
pcu/hour. It can be known the length of the queue that occurs, where the length of the queue that 
occurs depends on the volume of traffic, the length of the closure and the number of lanes that are 
closed. 

Keywords: Characteristics, Jagorawi toll road, Lane closure, Shock wave, Traffic flow. 

 
1. Introduction  

According to the Law of the Republic of Indonesia Number 2 Year 2022, the definition of a Toll 
Road is a Freeway which is part of the Road Network System and as a national road whose users are 
required to pay, while a Freeway is a Public Road for traffic with full control of the entrance road and 
without a level of intersection and equipped with a space fence belonging to the Road.   Toll roads are 
designed based on a minimum planned speed of 80 (eighty) kilometers per hour for intercity toll roads 
and 60 (sixty) kilometers per hour for toll roads in urban areas (Government Regulation 23 on Toll 
Roads, 2024).  

Reducing congestion and increasing productivity is a typical goal of highway transportation 
management and control initiatives. Travel time per vehicle, average speed, and total delay are three 
metrics that can be used to quantify the throughput of any instrumented freeway stretch in real-time 
(Chen et al., 2001). 

According to Dagazo (1995), continuum models of traffic flow are hyperbolic systems that describe 
how traffic states evolve based only on the initial and boundary conditions. Since they may use fluid-like 
state variables like density and flow to examine the collective behavior of traffic flow at an aggregate 
level, these models are also referred to as macroscopic models. Despite its simplicity, the LWR model of 
traffic flow is an incredibly strong and effective theory, however it is unable to explain significant traffic 
phenomena like vehicle clustering. In macroscopic traffic theory literature, particularly in higher order 
model literature (Gupta et al, 2005) 

 Greenshields, Greenberg and Underwood models are the most commonly used models to state the 
relationships between flow, density and speed. These models are key factors for traffic engineers to 



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explore the characteristic of traffic flow. The Greenshields model is considered as the best that 
represent the field data (Rompies, 2018) 

Shockwave is defined as the movement or journey of a change in traffic flow Shockwave in road 
traffic is described as a movement in traffic flow due to a change in density and traffic flow values. In the 
condition of free flow, if the current gets an obstacle (disturbance), there will be a reduction in the 
current that passes through the location of the obstacle. This reduction in flow results in congestion in 
the area before the obstacle increases, ultimately resulting in a decrease in speed and queues. (Tamin, 
2003). 

The implementation of toll roads must meet the Minimum Service Standards (SPM) of Toll Roads 
as regulated in the Regulation of the Minister of Public Works (PU) Number 16/PRT/M/2014, where 
the Minimum Service Standard for the average travel speed under normal conditions for intercity toll 
roads is >60 km/hour. This speed must be maintained so that obstacles that will reduce the speed of the 
vehicle must be overcome immediately. Obstacles that occur can be in the form of lane closures, 
accidents, road repairs, and so on. 

To find out the prediction of speed decrease due to obstacles on the freeway, it is necessary to study 
the characteristics of the flow of traffic on the road.  

This research was conducted on the JAGORAWI toll road, where the Jakarta-Bogor-Ciawi toll road 
is a connecting access from the city of Jakarta out of cities such as Bogor and the Puncak area. As a 
result, the JAGORAWI Toll Road every day demands a high-intensity movement so that it must be 
guaranteed to move as smoothly as possible. However, it is inevitable that there will be obstacles that 
occur such as accidents or road repairs that require the closure of part of the closed lane.  
 

2. Literature Review 
2.1. Traffic Flow Characteristics  

There are three main variables needed in analyzing traffic characteristics on road sections, namely 
volume, speed and density.  
The relationship between velocity, volume and density can be represented as follows: 

𝑄 = 𝑢. 𝑘 
where:  
Q =volume (kend/jam) 
u = speed (km/hour) 
k = density (kend/h) 

This relationship can also be illustrated with Figure 1 which shows the general relationship 
between velocity-density (u-k), volume-density (q-k) and volume-velocity (q-u). 
 

 
Figure 1.  
Fundamental diagram. 

In this study, there are 3 types of traffic flow models used to represent the mathematical 



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Edelweiss Applied Science and Technology 
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relationship between speed, volume, and density, namely Greenshields, Greenberg and Underwood. 
 
2.2. Model of the Relationship of Volume, Speed And Density  
2.2.1. Model Greenshield 

This modeling is the earliest model recorded in an effort to observe traffic behavior. Greenshields 
got the result that the relationship between velocity and density is linear. This model can be described 
as follows: 
Us = Uf – (Uf / Dj ) D  
Where 
Us: average speed of space (km/hour) 
Uf : speed in free flow conditions (km/hour) 
K : Density (pcu/km),  
Kj: jammed density (pcu/km)  
Q is the traffic flow (pcu/hour). 
Greenshield reveals the relationship between volume and density as follows: 
Q = Uf x D – (U/Dj) x D² 
The relationship between volume and velocity is also a parabolic relationship with the following form of 
equation: 
 
Q= Dj x Us – (Dj / Uf) x Us² 

In regression analysis, the correlation coefficient is a measure of the closeness of the relationship 
between free variables (x) and non-free variables (Q). The Coefficient of Determination (r2) is used to 
determine the extent to which the contribution of the free variable in the regression model is able to 
explain the variation of the bound variable. The coefficient equation of correlation (r) is as follows: 
 
 
 
 
2.3. Shock Wave 

Shockwave is defined as the movement or journey of a change in traffic flow Shockwave in road 
traffic is described as a movement in traffic flow due to a change in density and traffic flow values. 
Tamin, 2003). Shock waves can be described as movements in traffic flow due to changes in the density 
value of traffic flows when the current and density are relatively high. If an obstacle is given to the 
current, there will be a reduction in the current that can pass through the location of the obstacle. This 
reduction in flow results in the density of vehicles in the area before the location of the obstacle becomes 
high, which in the end the vehicle speed drops or even queues occur. The obstacle to traffic flow can be 
in the form of lane closure due to accidents, road repairs, or it can also occur due to traffic lights. 

In the following Figure 2, it shows the graph of the relationship between k and q. Point A is a traffic 
condition with a current of VA and a density of D. Point B is a traffic condition after experiencing an 
obstacle with a current of VB and a density of DB. Point B can be in the form of a closed lane of 1 lane 
or closed altogether. Point C is the maximum current condition i.e. after the resistance is removed. 
Point D is the point in front of the stop line, which shows VD = 0 and DD = 0. T is the time it takes 
from the beginning of lane normalization to the end of the queue. 



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Edelweiss Applied Science and Technology 
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Figure 2.  
Shock waves in road narrowing (Current-density). 

Source:  Tamin (2008). 

 

 
Figure 3.  
Shock waves in road narrowing (Time-distance). 

Source:  Tamin (2008). 

 
(T2 - T1) indicates the duration of the incident, 
(T3 - T2) is related to the total time from lane opening to the last time a vehicle joined a long queue. 
The total delay is the multiplication of the EFG triangle region by the density value associated with 
it and the FHG triangle multiplication region by the associated density value. 
 

3. Research Methods 
The research location is on the Jagorawi Toll Road KM 19+600. 



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Edelweiss Applied Science and Technology 
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Figure 4.  
Research location, Jagorawi toll road KM 19+600. 

 
The primary data obtained in this study was obtained directly from the results of the field 

survey, namely the Geometry Data of the Jagorawi Toll Road km19 + 600 measured at FO GT 
Cimanggis. As for the secondary, it was obtained from PT Jasamarga Jagorawi in the form of CCTV 
at km 19 + 600. 
 



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Edelweiss Applied Science and Technology 
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Figure 5.  
Flow chart of research methods. 

 
Traffic flow and vehicle speed are calculated with a predetermined distance guide. The density is 

calculated from the results of the flow analysis divided by the velocity. The analysis of the relationship 
between volume, velocity and density was carried out using the Greenshield model. After obtaining the 
flow-speed-density relationship model, shock wave analysis was carried out by simulating the closure of 
1,2 and 3 lanes.  
 

4. Results and Discussion 
In this study, the enumeration of traffic volume begins by determining a certain point or line on the 

video data from CCTV (Figure 6), then the enumeration of traffic volume based on the type of vehicle 
with a duration of 5 minutes.  

 
 
 
 



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Figure 6.  
Reference point for data collection of traffic volume and speed. 

 
Furthermore, the traffic volume is recorded and multiplied by the passenger car equivalent (emp). 

The total number of vehicles with the highest hours in the observation period is: 
Bogor Direction  : 6821 vehicles  
Jakarta Direction  :7414 vehicles  
Type of linemen                            : Flat 
The passenger car equivalent (pce) values used are: 
Passenger car   : 1.0 
Medium sized vehicle   : 1.3 
Big Bus    : 1.5 
Big Truck   : 2.0 

Based on this value, the traffic volume per 5 minutes can be converted to passenger car units (pcu). 
An example of the calculation of the results of the conversion from vehicle units per group to pcu in the 
observation period at 06.00-06.05 is presented in Table 1. 
 

Table 1.  
Traffic flow at 06.00-06.05 on  Jagorawi toll road km 19+600. 

Type  I Type  II Type  III Type  IV Type  V 5 minutes per hour

Bogor 150 16 15 1 0 195 2344

Jakarta 303 30 13 3 0 368 4410

directionPeriod
number of pcunumber of vehicle (vehicle)

06.00 - 

06.05  
Source:  Analysis Results, 2024. 

 
Traffic speed is obtained by measuring the travel time of each vehicle according to the type of 

vehicle so that the speed of each vehicle is obtained. The measurement of travel time begins by 
determining a 2(two) lines with a distance of 52 m obtained from the results of the field survey on the 
video data of the CCTV results. 



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Edelweiss Applied Science and Technology 
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The traffic density value is calculated using the formula for the relationship between volume 
and traffic speed as follows: 

K=
𝑸

𝑼
 

Where:  
K = Density (Number of vehicles/km) 
 Q = Traffic volume (pcu/hour) 
U = Average speed (Km/hour) 

The results of the calculation of speed, volume and traffic density on the Jagorawi toll road km 
19 + 600 for each 5-minute period are presented in Table 2 and Table 3, which are as follows: 
 

Table 2.  
Speed-volume-density Jl, Jagorawi toll road km 19+600 bogor direction. 

 
Source:  Analysis Results, 2024. 

 
 
 
 
 



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Table 3.  
Speed-volume-density Jl, Jagorawi toll road Km 19+600 Jakarta. 

average speed (u) flow rate (Q) density (k=Q/u)

km/hour pcu/hour pcu/km

1 75 4410 59

2 85 4722 55

3 69 3872 56

4 66 4518 69

5 58 5675 98

6 61 5573 92

7 72 5234 72

8 67 6217 93

9 69 6457 94

10 67 6654 99

11 76 5695 75

12 68 4811 71

13 58 6547 113

14 63 5424 86

15 65 5018 78

16 76 4589 60

17 77 5063 66

18 72 4684 65

19 79 4880 62

20 69 4068 59

21 63 4928 78

22 67 4300 65

23 64 7414 117

24 68 4576 67

25 80 4140 51

26 73 5156 70

27 71 4316 60

28 79 4590 58

no. of 

data

 
Source:  Analysis Results, 2024. 

 
4.1. Analysis of Volume, Velocity, and Density Relationship Models 

The calculation of the mathematical relationship for the Greenshield model is determined based on 
the combination of speed, volume and density data in both directions of Bogor and Jakarta to obtain 
more varied data on high and low traffic volume conditions. Merge is possible due to the same 
geometric dimensions in both directions 
 
4.1.1. Relationship Between Speed and Density 

Greenshield states that the relationship between velocity and density is in the form of a linear 
function with the equation: 

U.s.= 𝑈𝑓 − (
𝑈𝑓

𝐷𝑗
) . 𝐷 

Where 
U.s. : Speed (km/hour) 
Uf : Free flow speed (km/hour) 
Dj  : jammed density (pcu/km) 
D  : density (pcu/km) 
the equation is changed to a linear equation y = a + bx with Us = y,  
Uf = a, b = (-Uf/Dj), x = D. So it is obtained: 
a = 83.33, Maka Uf = a = 83.33 km/hour 
b = -0.1813, Maka Dj = Uf/b = 459.57pcu/hour 
The calculations a and b are presented in the Appendix. 
So the regression equation is 
Us = 83.33 – (0.1813) x D 

Its correlation coefficient (r)  =
𝑛(∑𝑋𝑌)−∑𝑋.∑𝑌

√(𝑛∑𝑋2−(∑𝑋)2)(𝑛.∑𝑌2−(∑𝑌)²
 

     = -0.9331 



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   r²  = 0.8707 

b. Volume and Speed Relationship 
The relationship between volume and velocity is a parabolic relationship with the following 

form of equation: 
V  = Dj x Us – (Dj / Uf) x Us² 
 = 459.57 x Us – (459.57 / 83.33) x Us² 

c. Relationship between volume and density 
The relationship between volume and density is also a parabolic relationship with the following 

form of equation: 
V  = Uf x D – (Uf / Dj) x D² 

= 83.33 x D – (0.1813) x D² 
The maximum Volume calculation can be calculated by using the formula  
Vmaks  = Uf x Dj / 4  

= 88.33 x 459.57 / 4 
 = 9574 smp / jam 

Based on the mathematical model of the relationship between velocity, volume and density, the 
capacity values for each model are presented in Table 4. Namely as follows: 
 

Table 4.  
Capacity calculation based on the mathematical model of speed, volume 
and density of the Jagorawi toll road km 19+600. 

 Capacity 

 Pcu/4 lanes/hr Pcu/lane/hr 
Model  9574 2393 
PKJI 10000 2500 

 
The mathematical model of the relationship between speed, volume and density of the Jagorawi 

toll road km 19 + 600 is presented in Table 5 and Figures 6, 7 and 8 as follows 
 

Table 5.  
Mathematical model of the relationship between speed, volume and density of the 
jagorawi toll road km 19+600 

Relationship Equation 
Speed-density Us= 83.33 – 0.1813D 

Flow-speed Q = 459.57Us-5.52Us2 
Flow-density Q = 83.33D – 0.1813D2 

Source:  Analysis Results, 2024. 

 
From the calculation results, it appears that all models are suitable for use because the value of 

r2  0.87 for all models is 8.87>0.8. So for the selection of the model to be used, the Greenshield model is 
because The maximum capacity value of the model Greenshield, which is 2393 pcu/hour/lane, is close 
to the Indonesia Road Capacity Guidelines (PKJI, 2023) of 2500 pcu/hour/lane. 
 



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Figure 7.  
Graph of the relationship between speed and density. 

 

 
Figure 8.  
Volume and speed relationship graph. 

 

0

10

20

30

40

50

60

70

80

90

0 50 100 150 200 250 300 350 400 463

Sp
e

e
d

 (
km

/h
o

u
r)

Density (pcu/km)

0

2000

4000

6000

8000

10000

12000

83 74 65 56 47 38 29 20 11 0

fl
o

w
 (

p
cu

/h
o

u
r)

Speed (km/hour)



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Figure 9.  
Volume and density relationship graph. 

 
4.2. Shock Wave 

The selection of the Greenshield model on the Jagorawi toll road section is set for the calculation of 
3 lanes at once with an observation interval of 5 minutes. The initial calculation is the Capacity Used 
Due to Lane Closure, which can be seen in Table 6 Table of Capacity Used Due to Lane Closure. 

 
Table 6.  
Capacity Used due to lane closure. 

effective 

width

base 

capacity 

effective 

capacity 

(meter) pcu/lane/hourpcu/hr

3.75 11.25 3 1.03 2500 7725

7.5 7.5 2 1.03 2500 5150

11.25 3.75 1 1.03 2500 2575

closed 

lane width 

(m)

no of 

lane

Factor of 

lane width

 
Source:  Analysis Results, 2024. 

 
4.3. Shock Wave Due to the Closure of 1 Lane 

The value of shock waves that occur on roads that are disrupted by the closure of 1 lane can be 
seen in the graph. 

 

0

2000

4000

6000

8000

10000

12000

0 50 100 150 200 250 300 350 400 463

fl
o

w
 (

p
cu

/h
o

u
r)

Density (pcu/km)



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Figure 10.  
1 Lane closure chart. 

 

 
Figure 11.  
Shock wave in the condition that the road is closed 1 lane closure for 5 minutes, for the value V = 7200 
pcu/hour 

V
o

lu
m

e 
(p

cu
/h

o
u

r)

Density (pcu/km)



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The state of traffic flow in condition A, is the traffic flow when entering condition B which is the 
condition of the traffic flow that is experiencing obstacles (1 lane is blocked) during the time between t0 

to t1, there is no obstacle in the traffic flow moving downstream with the flow of condition A (VA, DA). 
VA value is the value of the current that occurs in condition A.  

The value of VA = 7200 pcu/hour and the value of DA is the value of the density that occurs under 
condition A. The value of density DA follows the function of the mathematical relationship between 
current – density of the Greenshield model, which is 115.35 pcu/hour. The value of VA must be above 
the usable capacity of 1 lane.  

At the time of t1 (5 minutes), there was an obstacle that caused a narrowing or bottleneck effect and 
the traffic condition changed to condition B (VB, DB).  

VB is the current value that occurs in condition B. The value is taken from the calculation of the 
usable capacity for 1 lane in table 4.13, namely VB = 7107. And DB is the density value in condition B. The 
value of DB follows the function of the mathematical relationship between current – density of the 
Greenshield model. DB = 346.5 pcu/hour. 

After the occurrence of a downstream narrowing changes to condition D, Point D is the point in 
front of the stop line indicating zero current and zero density conditions. VD= 0, DD = 0. At the start of t 

1, the shock wave that occurs is ωAB. ωAB is the wave velocity between 2 (two) conditions A and B.  
Traffic flow in conditions A, B and D continues to occur until time t2 where at that time the traffic 

flow does not experience obstacles.  
In the C condition (VC, DC), it is the maximum current condition after the resistance is removed. 

Where the value of Vc is the maximum current value obtained from the mathematical function between 
current – density of the Greenshield model, namely VC = 9574 pcu/hour. And the DC value is the density 
that occurs at the maximum current according to the Greenshiled model, namely DC = 228 pcu/hour. 

At the time of the change of conditions to C, this causes the formation of 2 new shock waves, namely 

ωDC and ωCB. Traffic flow in conditions D, C, B and A continues until ωAB and ωCD reach t3. At time 

t3 1 (one) new shock wave is formed, namely the forward motion shock wave ωAC, and 2 (two) 

backward motion shock waves ωAB and ωCB end. And at t4, the forward motion shock wave ωAC cuts 
the stop line and the traffic current at the stop line changes from the maximum current Vc to Va. 

Example of a shock wave calculation on a toll road section that is closed 1 (one) lane for 5 minutes 
VA = 7200 pcu/hour,  DA = 115,35 pcu/hour,  
VB = 7107 pcu/hour,  DB = 346.5 pcu/hour, Value taken from capacity calculation Applies to 1 
column on Table 6. 
 

𝛚𝐀𝐁 =
𝑽𝑩 − 𝑽𝑨

𝑫𝑩 − 𝑫𝑨
=

𝟕𝟏𝟎𝟕 − 𝟕𝟐𝟎𝟎

𝟑𝟒𝟔, 𝟓 − 𝟏𝟏𝟓, 𝟑𝟓
= −𝟎, 𝟒𝟎𝟐 𝒌𝒎/𝒉𝒐𝒖𝒓 

 
A negative value indicates a backward movement. When there is no obstacle, the current 

changes to condition C. Backward moving shock wave is moving in the opposite direction to the 
movement of traffic flow (queue speed) 
VC = 9574pcu/hour,  DC = 228 pcu/hour 
 

𝛚𝐂𝐁 =
𝑽𝑩 − 𝑽𝑪

𝑫𝑩 − 𝑫𝑪
=

𝟕𝟏𝟎𝟕 − 𝟗𝟓𝟕𝟒

𝟑𝟒𝟔, 𝟓 − 𝟐𝟐𝟖
= −𝟐𝟎. 𝟖𝟏𝟗 𝒌𝒎/𝒉𝒐𝒖𝒓 

 
A negative sign means that the shock wave is moving backwards 
 

𝛚𝐃𝐂 =
𝑽𝑪 − 𝑽𝑫

𝑫𝑪 − 𝑫𝑫
=

𝟗𝟓𝟕𝟒 − 𝟎

𝟐𝟐𝟖 − 𝟎
= 𝟒𝟏. 𝟗𝟗𝟏 𝒌𝒎/𝒉𝒐𝒖𝒓 



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A positive sign means that the shock wave is moving forward (forward moving shock wave), 

which is moving in the same direction as the movement of traffic flow. With r = 5 minutes, then:  
 

𝐭𝟑 − 𝐭𝟐 =
𝒓

𝟔𝟎
 𝒙 (

𝝎𝑨𝑩

𝝎𝑩𝑪 −  𝝎𝑨𝑩
) =

𝟓

𝟔𝟎
𝒙 (

𝟎, 𝟒𝟎𝟐

𝟐𝟎, 𝟖𝟏𝟗 − 𝟎, 𝟒𝟎𝟐
) = 𝟎, 𝟎𝟎𝟐 𝒎𝒊𝒏𝒖𝒕𝒆 

 

𝐐𝐌 =
𝒓

𝟔𝟎
 𝒙 (

𝝎𝑪𝑩 𝒙 𝝎𝑨𝑩

𝝎𝑪𝑩 −  𝝎𝑨𝑩
) =

𝟓

𝟔𝟎
𝒙 (

𝟐𝟎, 𝟖𝟏𝟗 𝒙 𝟎, 𝟒𝟎𝟐

𝟐𝟎, 𝟖𝟏𝟗 −  𝟎, 𝟒𝟎𝟐
) 𝒙 𝟏𝟎𝟎𝟎 = 𝟑𝟒, 𝟏𝟗 𝒎𝒆𝒕𝒆𝒓 

 

𝛚𝐀𝐂 =
𝑽𝑪 − 𝑽𝑨

𝑫𝑪 − 𝑫𝑨
=

𝟗𝟓𝟕𝟒 − 𝟕𝟐𝟎𝟎

𝟐𝟐𝟖 − 𝟏𝟏𝟓, 𝟑𝟓
= 𝟐𝟏, 𝟎𝟕𝟒 𝒌𝒎/𝒉𝒐𝒖𝒓 

 

𝐭𝟒 − 𝐭𝟐 =
𝒓

𝟔𝟎
 𝒙 (

𝝎𝑨𝑩

𝝎𝑪𝑩 −  𝝎𝑨𝑩
) 𝒙 (

𝝎𝑪𝑩

𝝎𝑨𝑪
+ 𝟏) =

𝟓

𝟔𝟎
𝒙 (

𝟎, 𝟒𝟎𝟐

𝟐𝟎, 𝟖𝟏𝟗 − 𝟎, 𝟒𝟎𝟐
) 𝒙(

𝟐𝟎, 𝟖𝟏𝟗

𝟐𝟏, 𝟎𝟕𝟒
+ 𝟏)

= 𝟎, 𝟎𝟎𝟑 𝒎𝒆𝒏𝒊𝒕 
 
(t4 – t2) = T, called normalization time, which is the total time from the normalization of the lane to the 
end of the queue. 
 
Shock Wave Due to the Closure of 2 Lanes 

Example of a shock wave calculation on a toll road section that is closed 2 (two) lanes for 5 
minutes with a value of VA which is 7200 PCU/hour. 
VA = 7200 pcu/hour, DA = 115.35 pcu/hour 
VB = 4738 pcu/hour, DB = 393.15 pcu/hour, The value is taken from the capacity calculation 
applicable to 2 columns on Table 6. 
 

ωAB =
𝑉𝐵 − 𝑉𝐴

𝐷𝐵 − 𝐷𝐴
=

4738 − 7200

393,15 − 115,35
= −8,862 𝑘𝑚/ℎ𝑜𝑢𝑟 

 
A negative value indicates a backward movement. When there is no resistance, the current changes to 
condition C. 
VC = 9574pcu/hour, DC = 228 pcu/hour 
 

ωCB =
𝑉𝐵 − 𝑉𝐶

𝐷𝐵 − 𝐷𝐶
=

4738 − 9574

393,15 − 228
= −29,282 𝑘𝑚/ℎ𝑜𝑢𝑟 

 
A negative sign means that the shock wave is moving backwards 
 

ωDC =
𝑉𝐶 − 𝑉𝐷

𝐷𝐶 − 𝐷𝐷
=

9574 − 0

228 − 0
= 41.991 𝑘𝑚/ℎ𝑜𝑢𝑟 

 
A positive sign means that the shock wave is moving forward, with r = 5 minutes, then:  
 

t3 − t2 =
𝑟

60
 𝑥 (

𝜔𝐴𝐵

𝜔𝐵𝐶 −  𝜔𝐴𝐵
) =

5

60
𝑥 (

8,862

29,282 − 8,862
) = 0,036 𝑚𝑒𝑛𝑖𝑡 

 



937 

 

 

Edelweiss Applied Science and Technology 
ISSN: 2576-8484 

Vol. 8, No. 5: 922-939, 2024 
DOI: 10.55214/25768484.v8i5.1794 
© 2024 by the author; licensee Learning Gate 

 

QM =
𝑟

60
 𝑥 (

𝜔𝐶𝐵 𝑥 𝜔𝐴𝐵

𝜔𝐶𝐵 −  𝜔𝐴𝐵
) =

5

60
𝑥 (

29,282 𝑥 8,862

29,282 −  8,862
) 𝑥 1000 = 1059,08 𝑚𝑒𝑡𝑒𝑟 

 

ωAC =
𝑉𝐶 − 𝑉𝐴

𝐷𝐶 − 𝐷𝐴
=

9574 − 7200

228 − 115,35
= 21,074 𝑘𝑚/ℎ𝑜𝑢𝑟 

 

t4 − t2 =
𝑟

60
 𝑥 (

𝜔𝐴𝐵

𝜔𝐶𝐵 −  𝜔𝐴𝐵
) 𝑥 (

𝜔𝐶𝐵

𝜔𝐴𝐶
+ 1) =

5

60
𝑥 (

8,862

29,282 − 8,862
) 𝑥(

29,282

21,074
+ 1)

= 0,086 𝑚𝑒𝑛𝑖𝑡 
(t4 – t2) = T, called normalization time, which is the total time from the lane normalization to the end of 
the queue 
 
Shock Wave Due to 3-Lane Closure 

Example of a shock wave calculation on a toll road section that is closed 3 (three) lanes for 5 
minutes with a value of VA which is 7200 PCU/hour. 
VA = 7200 pcu/hour, DA = 115.35 pcu/hour 
VB = 2369 pcu/hour, DB = 429.18 pcu/hour. The value is taken from the capacity calculation 
Applicable to 3 columns on Table 4.13 
 

ωAB =
𝑉𝐵 − 𝑉𝐴

𝐷𝐵 − 𝐷𝐴
=

2369 − 7200

429,18 − 115,35
= −15,394 𝑘𝑚/ℎ𝑜𝑢𝑟 

 
A negative value indicates a backward movement. When there is no resistance, the current changes to 
condition C. 
VC = 9574pcu/hour, DC = 228 pcu/hour 
 

ωCB =
𝑉𝐵 − 𝑉𝐶

𝐷𝐵 − 𝐷𝐶
=

2369 − 9574

429,18 − 228
= −35,814 𝑘𝑚/ℎ𝑜𝑢𝑟 

 
A negative sign means that the shock wave is moving backwards 
 

ωDC =
𝑉𝐶 − 𝑉𝐷

𝐷𝐶 − 𝐷𝐷
=

9574 − 0

228 − 0
= 41.991 𝑘𝑚/ℎ𝑜𝑢𝑟 

 
A positive sign means that the shock wave is moving forward, with r = 5 minutes, then:  
 

t3 − t2 =
𝑟

60
 𝑥 (

𝜔𝐴𝐵

𝜔𝐵𝐶 −  𝜔𝐴𝐵
) =

5

60
𝑥 (

15,394

35,814 − 15,394
) = 0,063 𝑚𝑖𝑛𝑢𝑡𝑒 

 

QM =
𝑟

60
 𝑥 (

𝜔𝐶𝐵 𝑥 𝜔𝐴𝐵

𝜔𝐶𝐵 −  𝜔𝐴𝐵
) =

5

60
𝑥 (

35,814 𝑥 15,394

35,814 −  15,394
) 𝑥 1000 = 2249,85 𝑚𝑒𝑡𝑒𝑟 

 

ωAC =
𝑉𝐶 − 𝑉𝐴

𝐷𝐶 − 𝐷𝐴
=

9574 − 7200

228 − 115,35
= 21,074 𝑘𝑚/ℎ𝑜𝑢𝑟 

 



938 

 

 

Edelweiss Applied Science and Technology 
ISSN: 2576-8484 

Vol. 8, No. 5: 922-939, 2024 
DOI: 10.55214/25768484.v8i5.1794 
© 2024 by the author; licensee Learning Gate 

 

t4 − t2 =
𝑟

60
 𝑥 (

𝜔𝐴𝐵

𝜔𝐶𝐵 −  𝜔𝐴𝐵
) 𝑥 (

𝜔𝐶𝐵

𝜔𝐴𝐶
+ 1) =

5

60
𝑥 (

15,394

35,814 − 15,394
) 𝑥(

35,814

21,074
+ 1)

= 0,17 𝑚𝑒𝑛𝑖𝑡 
(t4 – t2) = T, called normalization time, which is the total time from the normalization of the lane to 

the end of the queue. 
Relationship between queue length and closing time with V=7200 pcu/hour due to 1, 2 and 3 lanes 

closure is shown on Figure 12. 
 

 
Figure 12.  
Relationship between queue length and closing time with V=7200 pcu/hour. 

 

5. Discussion 
1. On the Jagorawi toll road (8 lanes, 2 directions) KM 19 + 600, the flow-speed-density 

relationship equation with a very strong relationship was obtained, a capacity value of 9574 
pcu/hour/4 lanes was obtained 

2. If 1 lane is closed on the Jagorawi toll road at traffic flow q = 7200 pcu/hour, the length of the 
queue that occurs during the 5-minute closure period is 34.19 meters. If it is closed for 120 
minutes, there will be a queue length of 820.53 meters.  

3. If the closure of 2 lanes on the Jagorawi toll road is carried out at traffic flow q = 7200 
pcu/hour, the length of the queue that occurs during the 5-minute closure period is 1059.08 
meters. If it is closed for 120 minutes, there will be a queue length of 25417.82 meters.  

4. If the closure of 3 lanes on the Jagorawi toll road is carried out at traffic flow q = 7200 
pcu/hour, the length of the queue that occurs during the 5-minute closure period is 2249.85 
meters. If it is closed for 120 minutes, there will be a queue length of 53996.51 meters.  

 

6. Conclusion 
The relationship between speed – density, flow relationship – density, and the relationship between 

flow and speed on the Jagorawi KM 19+600 toll road from the Greenshield model has a strong 
coefficient of determination.  

From the results of the shock wave simulation for the closure of 1 lane, 2 lanes and 3 lanes with the 

1 lane closure 2 lanes closure 3 lanes closure1 lane closure



939 

 

 

Edelweiss Applied Science and Technology 
ISSN: 2576-8484 

Vol. 8, No. 5: 922-939, 2024 
DOI: 10.55214/25768484.v8i5.1794 
© 2024 by the author; licensee Learning Gate 

 

same flow, it can be known the length of the queue that occurs, where the length of the queue that 
occurs depends on the traffic volume, the length of the closure and the number of lanes closed. 

 
Copyright:  
© 2024 by the authors. This article is an open access article distributed under the terms and conditions 
of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). 
 

References 
[1] C. Chen et al, 2001, Freeway performance measurement system: mining loop detector data, Transportation Research Record Journal 

of the Transportation Research Board 

[2] Dagazo C.F, 1997, A Continuum Theory of Traffic Dynamics For Freeways With Special Lanes, Transportation Research Part 
B: Methodological, Volume 31, Issue 2, April 1997, Pages 83-102 

[3] Gupta A & Katiyar V.K, 2005, Analyses of shock waves and jams in traffic flow, Journal of Physics A Mathematical and General 
38(19):4069 

[4] Kementerian Pekerjaan Umum dan Perumahan Rakyat, Peraturan Menteri PUPR No. 16 
tahun 2014 Tentang Standar Pelayanan Minimal Jalan Tol, Berita Negara RI 2014 No. 

[5] Peraturan Pemerintah (PP) Nomor 23 Tahun 2024 tentang Jalan Tol 
[6] Tamin, O.Z, (2000), Perencanaan dan Pemodelan Transportasi, Penerbit ITB Bandung  
[7] Tamin, O.Z, (2003), Perencanaan dan Pemodelan Transportasi, Edisi Pertama, Soal dan 

Aplikasi, Penerbit ITB, Bandung.  
[8] Undang-Undang Republik Indonesia Nomor 2 Tahun 2022 Tentang Perubahan Kedua Atas Undang-Undang Nomor 38 Tahun 

2004 Tentang Jalan 
[9] Peraturan Pemerintah Republik Indonesia Nomor 23 Tahun 2024 Tentang Jalan Tol 
[10] Peraturan Menteri Pekerjaan Umum (PU) tentang Standar Minimal Jalan tOl Tol Nomor 16/PRT/M/2014, 
[11] Rompies Semuel Y.R, 2018, Traffic Flow Model And Shockwave Analysis. Jurnal Sipil Statik Vol.6 No.1 Januari 2018 (13-20) ISSN: 

2337-6732 pp 13-20 

 
 
 
 
 
 
 

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